I agree about direct seeding your swiss chard into the ground. They are pretty cold hardy, so we usually say "as soon as the ground can be worked." That's when the ground is unfrozen (at least the top few inches!) and isn't too wet (doesn't all clump up when you try to turn it with a trowel).
For me that tends to be about a month ahead of my average last frost date.
If your in zone 4, like me I would start them inside. That way they can even have a good growing start, and since it can get hot very quick, having that quick start is crucial. You could start them in April sometime and get them out middle to late May.
I have terrible luck getting chard and beets (same plant, different growth forms) to start in my rough garden soil. If they do germinate they get cut down by slugs. Luckily, both can be started inside and transplanted when they get true leaves started.
I just separated some beet and S. chard seedling multiples yesterday. It's do-able after their seed leaves grow out (about 1wk after germination), but not much later -- the roots will be too tangled. But, really, it's not strictly necessary. I was just doing it for fun.
What can I say, jal_ut? Those are incredible...uh...beets! I was lucky to get a few beet greens last year, but have a theory as to why they were such a...bust. As with so much else in my yard, not enough sun...
I love seeing your successful garden and the incredible backdrop! Are those the Wasatch Mountains? The Grand Staircase?